This is a problem from Temple University's 'Calculus on the Web' site, I am trying to get re-acquainted with first-semester Calculus as I will begin taking Calc II in a month from now. I can't think of how to bring that x down. Logs?

jimmy_boots wrote:Find the limit, as x approaches infinity, of (1+(2/x))x

This is a problem from Temple University's 'Calculus on the Web' site, I am trying to get re-acquainted with first-semester Calculus as I will begin taking Calc II in a month from now. I can't think of how to bring that x down. Logs?

Do you need to bring it down?

If you plug infinity into x, starting from inside the parentheses and working outwards, what do you end up with?

jimmy_boots wrote:I follow the L'Hopital's Rule method of solving this problem, but where did you get the "" from?

This is a given identity thinger I should be familiar with? I haven't come across it, please let me know the deal.

This is just one of many ways of representing . It would be unreasonable to learn them all by heart, but a familiarisation with their general forms may alert you to the possibility of hiding in a particular problem. Learning a few of the simpler ones, like this, may prove useful (and save a lot of time).

In fact, by using the more general version of this representation of , the second solution can be simplified further:

Q. Find

Since ,

Therefore, .

Thinking about where this question originally came from, Temple University's 'Calculus on the Web' site, and the simplicity of the other 22 questions leading up to this one, I would imagine that the question may be testing for knowledge of this very representation of .